I have a small issue with DosBox games in Windows 10 and I'd like some help please.

Whenever I start the game it shows a black screen interrupted by part of the window behind {see start screen attachment}.
Whenever there is a transition between gameplay and a cutscene it shows either a cursor divided in two parts, or the last played scene before cutscene (like the screen is split into two and the colors are inverted). {see transition attachment}
And finally when I choose to exit the game, there is a screen before it returns back to the desktop. {see exit screen attachment}

None of these affect the overall gameplay, but I'd like to get rid of them anyway.
When I had Windows Vista none of that ever happened. Just a black screen between start, transitions and exit screens and that's all.
Furthermore , in Vista there was an option "disable Visual themes", or "disable Desktop composition" which helped for situations like this. But now there is no such option in Windows 10.

Is there a way to fix that? Maybe by changing something in dosbox.conf?

I am far from an expert in DOSBox, but I would experiment with the value for and see if that changes anything. Maybe change the [url=http://www.dosbox.com/wiki/Configuration#.5Brender.5D]scaler too.

Output is set to ddraw. Not all games react well if I change it to opengl. Actually the only game I've manage to run with opengl was Darklight Conflict. The rest simply crashed DosBox. Surface and Overlay are no different than ddraw.

And Scaler is either on normal2x or hq3x. No changes from there either.

Post the DOSBox version used. Should at the minimum be 0.74.
Post system specs including video driver version
If using non-default dosbox.conf then use the original.
Post name of the game or games.

You can't disable DWM in Windows 10.

My current system is an ASUS laptop, RoG model - G752VL with:
Windows 10 - 64bit
Intel i7
NVIDIA GeForce GTX 965M 2Gb
8Gb RAM
1TB HDD

and I'm using the latest drives from NVIDIA:
Version: 381.89 WHQL
Release Date: 2017.4.25

My old system was a Toshiba laptop, QOSMIO model - F50-10K with:
Windows Vista - 32bit
Intel Core Duo
NVIDIA Geforce 9600M GT 512Mb
4Gb RAM
650GB HDD

The games I've experienced this issue so far are:
Crusader: No remorse
Star Trek TNG: A Final Unity
Cyberia
C & C: Red Alert
Star Wars: Rebel Assault II
Star Wars : Dark Forces
Megarace II
Phantasmagoria 1+2
Harvester
Lost Eden
Blood

(well Crusader: No remorse has another issue with the sound, which I've posted it separately and I still haven't found the solution
and Blood refuses to play the intro video and gameplay is laggy for some reason - but that happened in both my systems
and my main concern right now is to find out why does it do that thing between transitions).

I'm pretty sure that it has to do with the desktop's composition. Desktop is running on a 1920x1080 resolution and that's not normal for such old games.
But without the disable Desktop composition option that cannot be changed.

Does it happen in both full-screen and windowed mode?

I recommend asking at the VOGONS forum, which has the official DOSBox support forum.